It's a Remake and Not a Remaster
So, this is pretty general, but Tony Hawk's Pro Skater 1+2 is a great example of showing the difference between a "remake" and a "remaster". This game is a remake. So, this basically means that you'll see all of the same levels you know and love from the OG Tony Hawk games, but they look more polished.
As an example, the iconic Warehouse level now features larger windows and more noticeable signs. The original was a bit darker due to tiny windows. Now it's more bright, with the lovely sunlight piercing through the old, abandoned structure. Heck, you'll even see a cat run by the window too.
So there are not only graphical improvements but just overall level improvements too. If it was a remaster, the levels would look exactly the same (which isn't a bad thing) but just with some better graphics. And the levels in this remake are extra vibrant, making the skateboarding experience that much more fun, and breathtaking as well.
Since it's been so long, one thing that wasn't present in the original two Tony Hawk games was a good, solid online mode. Tony Hawk's Pro Skater 1+2 now gives you the ability to scratch that competitive itch. There are two different modes, but the most popular and active is "Playlists".
This is a fun collection of modes that you play against other skaters around the globe. They're all score-based challenges except for the Grafitti mode. The adrenaline of a time limit and seeing other skaters all around you performing makes things quite interesting.
It's also pretty relaxing just playing each game on the playlist's rotation. Once one mode finishes, you move on to the next and after a few times on one level, you are switched off to a different level at random. So the overall flow is great. If you really want to compete, then there is a "Competitive" online mode where you play against some of the best virtual skaters out there.
To be completely honest, the character appearance customization isn't the deepest in Tony Hawk's Pro Skater 1+2, but it's enough to make yourself a cool-looking skater. Also, the amount of apparel, skateboards, etc you can get is great. You can unlock most of the gear by just playing through the game.
The good thing is that you don't need to stick with one specific mode to level up. Play whatever you want and get that number up. You'll be rewarded with some fresh new stuff. This will make you want to play more and level up. There are even animated skateboard designs you can get.
The popular Create-a-Park mode from Tony Hawk's Pro Skater 2 is also present in the remake. This adds to the replay value of the game. The online modes and Single Sessions are already enough to get the game fired up again so this just adds an extra topping to the skateboarding pizza.